This report describes SP, a system for specialising logic programs. The report functions as a user's manual for SP, and also contains the algorithms employed and arguments for their correctness. A number of examples of program specialisation are given in Appendix A. Contents 1 Program Specialisation 4 2 Transformations in SP 5 3 Unfolding Rules 10 4 Approximation 13 5 The Specialisation Algorithm 16 6 How to Use SP 20 7 Discussion 23 A Examples of Specialisation 28 B Unfoldability Conditions for Built-ins 36 1 Program Specialisation SP is a system for specialising logic programs. Before describing the system, it is worth reviewing briefly the aims and interesting applications of program specialisation. To specialise a program is to restrict its behaviour in some way. The purpose of specialisation is to exploit the restriction to gain efficiency. A specialised program is equivalent, within the bounds of the restriction imposed, to the original unspecialised program, but should be ...

Abstract. We generalize the various path orderings and the conditions under which they work, and describe an implementation of this general ordering. We look at methods for proving termination of orthogonal systems and give a new solution to a problem of Zantema's. 1

Languages that integrate functional and logic programming with a complete operational semantics are based on narrowing, a unification-based goal-solving mechanism which subsumes the reduction principle of functional languages and the resolution principle of logic languages. Formal methods of transformation of functional logic programs can be based on this well-established operational semantics. In this paper, we present a partial evaluation scheme for functional logic languages based on an automatic unfolding algorithm which builds narrowing trees. We study the semantic properties of the transformation and the conditions under which the technique terminates, is sound and complete, and is also generally applicable to a wide class of programs. We illustrate our method with several examples and discuss the relation with Supercompilation and Partial Evaluation. To the best of our knowledge this is the first formal approach to partial evaluation of functional logic programs.

The control of polyvariance is a key issue in partial deduction of logic programs. Certainly, only finitely many specialised versions of any procedure should be generated, while, on the other hand, overly severe limitations should not be imposed. In this paper, well-founded orderings serve as a starting point for tackling this so-called "global termination" problem. Polyvariance is determined by the set of distinct "partially deduced" atoms generated during partial deduction. Avoiding ad-hoc techniques, we formulate a quite general framework where this set is represented as a tree structure. Associating weights with nodes, we define a well-founded order among such structures, thus obtaining a foundation for certified global termination of partial deduction. We include an algorithm template, concrete instances of which can be used in actual implementations, prove termination and correctness, and report on the results of some experiments. Finally, we conjecture that the proposed framewor...

Abstract. Recently, considerable advances have been made in the (online) control of logic program specialisation. A clear conceptual distinction has been established between local and global control and on both levels concrete strategies as well as general frameworks have been proposed. For global control in particular, recent work has developed concrete techniques based on the preservation of characteristic trees (limited, however, by a given, arbitrary depth bound) to obtain a very precise control of polyvariance. On the other hand, the concept of an m-tree has been introduced as a refined way to trace “relationships ” of partially deduced atoms, thus serving as the basis for a general framework within which global termination of partial deduction can be ensured in a non ad hoc way. Blending both, formerly separate, contributions, in this paper, we present an elegant and sophisticated technique to globally control partial deduction of normal logic programs. Leaving unspecified the specific local control one may wish to plug in, we develop a concrete global control strategy combining the use of characteristic atoms and trees with global (m-)trees. We thus obtain partial deduction that always terminates in an elegant, non ad hoc way, while providing excellent specialisation as well as fine-grained (but reasonable) polyvariance. We conjecture that a similar approach may contribute to improve upon current (on-line) control strategies for functional program transformation methods such as (positive) supercompilation. 1

data types are facilitated in Godel by its type and module systems. Thus, in order to describe the meta-programming facilities of Godel, a brief account of these systems is given. Each constant, function, predicate, and proposition in a Godel program must be specified by a language declaration. The type of a variable is not declared but inferred from its context within a particular program statement. To illustrate the type system, we give the language declarations that would be required for the program in Figure 1. BASE Name. CONSTANT Tom, Jerry : Name. PREDICATE Chase : Name * Name; Cat, Mouse : Name. Note that the declaration beginning BASE indicates that Name is a base type. In the statement Chase(x,y) !- Cat(x) & Mouse(y). the variables x and y are inferred to be of type Name. Polymorphic types can also be defined in Godel. They are constructed from the base types, type variables called parameters, and type constructors. Each constructor has an arity 1 attached to it. As an...

Partial evaluation is a method for program specialization based on fold/unfold transformations [8, 25]. Partial evaluation of pure functional programs uses mainly static values of given data to specialize the program [15, 44]. In logic programming, the so-called static/dynamic distinction is hardly present, whereas considerations of determinacy and choice points are far more important for control [12]. We discuss these issues in the context of a (lazy) functional logic language. We formalize a two-phase specialization method for a non-strict, first order, integrated language which makes use of lazy narrowing to specialize the program w.r.t. a goal. The basic algorithm (first phase) is formalized as an instance of the framework for the partial evaluation of functional logic programs of [2, 3], using lazy narrowing. However, the results inherited by [2, 3] mainly regard the termination of the PE method, while the (strong) soundness and completeness results must be restated for the lazy strategy. A post-processing renaming scheme (second phase) is necessary which we describe and illustrate on the well-known matching example. This phase is essential also for other non-lazy narrowing strategies, like innermost narrowing, and our method can be easily extended to these strategies. We show that our method preserves the lazy narrowing semantics and that the inclusion of simplification steps in narrowing derivations can improve control during specialization.

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. Recently, partial deduction of logic programs has been extended to conceptually embed folding. To this end, partial deductions are no longer computed of single atoms, but rather of entire conjunctions; Hence the term "conjunctive partial deduction". Conjunctive partial deduction aims at achieving unfold/fold-like program transformations such as tupling and deforestation within fully automated partial deduction. However, its merits greatly surpass that limited context: Also other major efficiency improvements are obtained through considerably improved side-ways information propagation. In this extended abstract, we investigate conjunctive partial deduction in practice. We describe the concrete options used in the implementation(s), look at abstraction in a practical Prolog context, include and discuss an extensive set of benchmark results. From these, we can conclude that conjunctive partial deduction indeed pays off in practice, thoroughly beating its conventional precursor on a wide...

Introduction: What is partial evaluation? Partial evaluation is a technique to partially execute a program, when only some of its input data are available. Consider a program p requiring two inputs, x 1 and x 2 . When specific values d 1 and d 2 are given for the two inputs, we can run the program, producing a result. When only one input value d 1 is given, we cannot run p, but can partially evaluate it, producing a version p d1 of p specialized for the case where x 1 = d 1 . Partial evaluation is an instance of program specialization, and the specialized version p d1 of p is called a residual program. For an example, consider the following C function p